Question

pls solve this.......​

Answer 1

(1) is the correct answer. because in series combination net K is equal to sum of squares of other k
T= 2π √(m/k)
since it is in series then K will be sum of other two
for t it will be square of other two

Answer 2

correct option is (b)

explaination :

the time period of a spring mass system as shown in figure 1 is

figure

given by T= 2π√m/k where k is spring constant.

therefore t1=2π√m/k1 ...(I)

and t2=2π√m/k2. ...(ii )

make figure here 2

now when they connected in parallel as shown in figure 2(a), the system can be replaced.by a single spring of spring constant , keff=k1+k2

[since mg = k1x +k2x =keff x]

therefore t0= 2π√m/keff = 2π√m/(k1+k2) ...(iii)

from(I) ,1/t1 square =1/4πsquare x k1 /m(iv)

from (ii) 1/t0square +1/t2square x k2/m

from ...(iii) 1/t0square=1/4π square x k1+k2/m...(vi)

(iv) + (v) =1/t1square +1/t2square=1/4π2m(k1+k2)=1/t0square

therefore t0-2.= t1-2+ t2-2